How hard is 3-view triangulation really?

We present a solution for optimal triangulation in three views. The solution is guaranteed to find the optimal solution because it computes all the stationary points of the (maximum likelihood) objective function. Internally, the solution is found by computing roots of multivariate polynomial equations, directly solving the conditions for stationarity. The solver makes use of standard methods from computational commutative algebra to convert the root-finding problem into a 47 /spl times/ 47 nonsymmetric eigenproblem. Although there are in general 47 roots, counting both real and complex ones, the number of real roots is usually much smaller. We also show experimentally that the number of stationary points that are local minima and lie in front of each camera is small but does depend on the scene geometry.